Trigonometric Identities

studied byStudied by 0 people
0.0(0)
learn
LearnA personalized and smart learning plan
exam
Practice TestTake a test on your terms and definitions
spaced repetition
Spaced RepetitionScientifically backed study method
heart puzzle
Matching GameHow quick can you match all your cards?
flashcards
FlashcardsStudy terms and definitions

1 / 96

encourage image

There's no tags or description

Looks like no one added any tags here yet for you.

97 Terms

1

cscθ

knowt flashcard image
New cards
2

secθ

knowt flashcard image
New cards
3

tanθ

knowt flashcard image
New cards
4

cotθ

knowt flashcard image
New cards
5

sin²θ

knowt flashcard image
New cards
6

cos²θ

knowt flashcard image
New cards
7

1

knowt flashcard image
New cards
8

cot²θ

knowt flashcard image
New cards
9

csc²θ

knowt flashcard image
New cards
10

sec²θ

knowt flashcard image
New cards
11

tan²θ

knowt flashcard image
New cards
12

sinθ

1/cscθ

New cards
13

cosθ

1/secθ

New cards
14

secθ reciprocal identity

1/cosθ

New cards
15

cscθ reciprocal identity

1/sinθ

New cards
16

cotθ reciprocal identity

1/tanθ

New cards
17

tanθ quotient identity

sinθ/cosθ

New cards
18

cotθ quotient identity

cosθ/sinθ

New cards
19

-sinθ odd-even identity

sin(-θ)

New cards
20

cosθ odd-even identity

cos(-θ)

New cards
21

-tanθ odd-even identity

tan(-θ)

New cards
22

-cscθ odd-even identity

csc(-θ)

New cards
23

secθ odd-even identity

sec(-θ)

New cards
24

-cotθ odd-even identity

cot(-θ)

New cards
25

sinθ cofunction identity

cos (π/2-θ)

New cards
26

cosθ cofunction identity

sin (π/2-θ)

New cards
27

tanθ cofunction identity

cot (π/2-θ)

New cards
28

cscθ cofunction identity

sec (π/2-θ)

New cards
29

secθ cofunction identity

csc (π/2-θ)

New cards
30

cotθ cofunction identity

tan (π/2-θ)

New cards
31

sin²θ + cos²θ Pythagorean identity

1

New cards
32

1 + tan²θ Pythagorean identity

sec²θ

New cards
33

1 + cot²θ Pythagorean identity

csc²θ

New cards
34

sin(α + β) sum identity

sinαcosβ + cosαsinβ

New cards
35

sin(α - β) difference identity

sinαcosβ - cosαsinβ

New cards
36

cos(α + β) sum identity

cosαcosβ - sinαsinβ

New cards
37

cos(α - β) difference identity

cosαcosβ + sinαsinβ

New cards
38

tan(α + β) sum identity

tanα + tanβ/1 - tanαtanβ

New cards
39

tan(α - β) difference identity

tanα - tanβ/1 + tanαtanβ

New cards
40

sin 2θ double-angle identity

2 sinθcosθ

New cards
41

cos 2θ double-angle identity

cos²θ - sin²θ

2 cos²θ - 1

1 - 2 sin²θ

New cards
42

tan 2θ double-angle identity

2 tanθ/1 - tan²θ

New cards
43

sin½θ half-angle identity

±√1 - cosθ/2

New cards
44

cos½θ half-angle identity

±√1 + cosθ/2

New cards
45

tan½θ half-angle identity

±√1 - cosθ/1 + cosθ

New cards
46

1/sin x

csc x

New cards
47

1/cos x

sec x

New cards
48

1/tan x

cot x

New cards
49

1/csc x

sin x

New cards
50

1/sec x

cos x

New cards
51

1/cot x

tan x

New cards
52

sin²x+cos²x

1

New cards
53

1-cos²x

sin²x

New cards
54

1-sin²x

cos²x

New cards
55

1+tan²x

sec²x

New cards
56

1+cot²x

csc²x

New cards
57

sec²x-1

tan²x

New cards
58

csc²x-1

cot²x

New cards
59

sin(-x)

-sin x

New cards
60

csc(-x)

-csc x

New cards
61

cos(-x)

cos x

New cards
62

sec(-x)

sec x

New cards
63

tan(-x)

-tan x

New cards
64

cot(-x)

-cot x

New cards
65

sin(π/2-x)

cos x

New cards
66

cos(π/2-x)

sin x

New cards
67

tan(π/2-x)

cot x

New cards
68

csc(π/2-x)

sec x

New cards
69

sec(π/2-x)

csc x

New cards
70

cot(π/2-x)

tan x

New cards
71

sin x / cos x

tan x

New cards
72

cos x/ sin x

cot x

New cards
73

Identity (math)

A mathematical statement or equation that is true for any value.

<p>A mathematical statement or equation that is true for any value.</p>
New cards
74

Pythagorean Identities

A trigonometric identity that is derived using the Pythagorean Theorem.

a² + b² = c²

x² + y² = r²

sin²θ + cos²θ = 1 (y=sin, x=cos, r=1 on unit circle)

1 + cot²θ = csc²θ (divide everything by sin²θ)

tan²θ + 1 = sec²θ (divide everything by cos²θ)

<p>A trigonometric identity that is derived using the Pythagorean Theorem.</p><p>a² + b² = c²</p><p>x² + y² = r²</p><p>sin²θ + cos²θ = 1 (y=sin, x=cos, r=1 on unit circle)</p><p>1 + cot²θ = csc²θ (divide everything by sin²θ)</p><p>tan²θ + 1 = sec²θ (divide everything by cos²θ)</p>
New cards
75

Quotient

The answer to a division problem.

<p>The answer to a division problem.</p>
New cards
76

Quotient Identities

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

<p>tanθ = sinθ/cosθ</p><p>cotθ = cosθ/sinθ</p>
New cards
77

Reciprocal

One of a pair of numbers whose product is 1.

<p>One of a pair of numbers whose product is 1.</p>
New cards
78

Reciprocal Identities

knowt flashcard image
New cards
79

Expression

A mathematical statement (variables,numbers, and operation symbols) that does not contain an equal sign.

<p>A mathematical statement (variables,numbers, and operation symbols) that does not contain an equal sign.</p>
New cards
80

Equation

A mathematical statement that two expressions are equal.

<p>A mathematical statement that two expressions are equal.</p>
New cards
81

Verify

To confirm or prove something is true.

<p>To confirm or prove something is true.</p>
New cards
82

Simplify

To make something easier or less complicated.

<p>To make something easier or less complicated.</p>
New cards
83

Solve

To find an answer to or explanation for a problem.

<p>To find an answer to or explanation for a problem.</p>
New cards
84

Evaluate

For a specific input, find the numerical output of an function. Plug a number in to get a solution.

<p>For a specific input, find the numerical output of an function. Plug a number in to get a solution.</p>
New cards
85

Isolate

To get a variable alone in a mathematical equation.

<p>To get a variable alone in a mathematical equation.</p>
New cards
86

Factor (verb)

To find the factors of a number or expression.

<p>To find the factors of a number or expression.</p>
New cards
87

Factor (noun)

A number which divides into another number exactly without leaving a remainder.

<p>A number which divides into another number exactly without leaving a remainder.</p>
New cards
88

Distribute (Expand)

Multiplying each term inside the parentheses with the term outside of the parentheses.

<p>Multiplying each term inside the parentheses with the term outside of the parentheses.</p>
New cards
89

Combine Like Terms

Simplifying an expression by using mathematical operations of terms with the same variables and exponents.

<p>Simplifying an expression by using mathematical operations of terms with the same variables and exponents.</p>
New cards
90

Coefficient

A number multiplied by a variable in an algebraic expression.

<p>A number multiplied by a variable in an algebraic expression.</p>
New cards
91

Variable

A letter or symbol used to represent numbers in Algebra.

<p>A letter or symbol used to represent numbers in Algebra.</p>
New cards
92

Constant

A value that does not change.

<p>A value that does not change.</p>
New cards
93

Radical

Another name for a root: one might refer to √2 as "radical 2."

<p>Another name for a root: one might refer to √2 as "radical 2."</p>
New cards
94

Undefined

Having no solution.

(Examples: dividing by zero, negative square roots, the slope of a vertical line)

New cards
95

Domain

All the possible x-values that can be input into a function.

New cards
96

Range

All the possible y-values that can be the output of a function.

New cards
97

Inverse Function

The function obtained by switching the domain (x) and range (y) in a function.

New cards

Explore top notes

note Note
studied byStudied by 102 people
1036 days ago
5.0(3)
note Note
studied byStudied by 7 people
893 days ago
5.0(1)
note Note
studied byStudied by 18 people
841 days ago
5.0(1)
note Note
studied byStudied by 9 people
874 days ago
5.0(1)
note Note
studied byStudied by 7 people
99 days ago
5.0(1)
note Note
studied byStudied by 156 people
374 days ago
5.0(1)

Explore top flashcards

flashcards Flashcard (30)
studied byStudied by 28 people
325 days ago
5.0(1)
flashcards Flashcard (27)
studied byStudied by 7 people
402 days ago
5.0(1)
flashcards Flashcard (120)
studied byStudied by 1 person
110 days ago
5.0(1)
flashcards Flashcard (31)
studied byStudied by 59 people
341 days ago
5.0(1)
flashcards Flashcard (65)
studied byStudied by 3 people
775 days ago
5.0(2)
flashcards Flashcard (115)
studied byStudied by 1109 people
406 days ago
5.0(2)
flashcards Flashcard (64)
studied byStudied by 14 people
754 days ago
4.0(1)
flashcards Flashcard (46)
studied byStudied by 3 people
1 day ago
5.0(2)
robot